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Factors of 103: Prime Factorization, Methods, and Examples

The factors of 103 are the numbers that leave zero as a remainder when 103 is divided from such numbers. These divisors are hence termed as the factors of that number.

The factors of 103 are only two because the number 103 is a prime number. Hence, its only factors are 1 and 103. 

Factors of 103

Here are the factors of number 103.

Factors of 103: 1 and 103

Negative Factors of 103

The negative factors of 103 are similar to its positive factors, just with a negative sign.

Negative Factors of 103: -1 and -103

Prime Factorization of 103

The prime factorization of 103 is expressing its prime factors in the form of the product.

Prime Factorization: 1 x 103

In this article, we will learn about the factors of 103 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 103?

The factors 103 are 1 and 103. All of these numbers are the factors as they do not leave any remainder when divided by 103.

The factors of 103 are classified as prime numbers and composite numbers. The prime factors of the number 103 can be determined using the technique of prime factorization.

How To Find the Factors of 103?

You can find the factors of 103 by using the rules of divisibility. The rule of divisibility states that any number when divided by any other natural number then it is said to be divisible by the number if the quotient is the whole number and the resulting remainder is zero.

To find the factors of 103, create a list containing the numbers that are exactly divisible by 103 with zero remainders. One important thing to note is that 1 and 103 are the 103’s factors as every natural number has 1 and the number itself as its factor.

1 is also called the universal factor of every number. The factors of 103 are determined as follows:

\[\dfrac{103}{1} = 103\]

\[\dfrac{103}{103} = 1\]

Therefore, 1 and 103 are the factors of 103.

Total Number of Factors of 103

For 103 there are 2 positive factors and 2 negative ones. So in total, there are 4 factors of 103. 

To find the total number of factors of the given number, follow the procedure mentioned below:

  1. Find the factorization of the given number.
  2. Demonstrate the prime factorization of the number in the form of exponent form.
  3. Add 1 to each of the exponents of the prime factor.
  4. Now, multiply the resulting exponents together. This obtained product is equivalent to the total number of factors of the given number.

By following this procedure the total number of factors of 103 is given as:

Factorization of 103 is 1 x 103.

The exponent of 1 and 103 is 1.

Adding 1 to each and multiplying them together results in 2.

Therefore, the total number of factors of 103 is 4 of which 2 are positive and 2 are negative.

Important Notes

Here are some important points that must be considered while finding the factors of any given number:

  • The factor of any given number must be a whole number.
  • The factors of the number cannot be in the form of decimals or fractions.
  • Factors can be positive as well as negative.
  • Negative factors are the additive inverse of the positive factors of a given number.
  • The factor of a number cannot be greater than that number.
  • Every even number has 2 as its prime factor which is the smallest prime factor.

Factors of 103 by Prime Factorization

The number 103 is a prime number. Prime factorization is a useful technique for finding the number’s prime factors and expressing the number as the product of its prime factors.

Before finding the factors of 103 using prime factorization, let us find out what prime factors are. Prime factors are the factors of any given number that are only divisible by 1 and themselves.

To start the prime factorization of 103, start dividing by its smallest prime factor. First, determine that the given number is either even or odd. If it is an even number, then 2 will be the smallest prime factor.

Continue splitting the quotient obtained until 1 is received as the quotient. The prime factorization of 103 can be expressed as:

\[ 103 = 1 \times 103\]

Factors of 103 in Pairs

The factor pairs are the duplet of numbers that when multiplied together result in the factorized number. Depending upon the total number of factors of the given numbers, factor pairs can be more than one.

For 103, the factor pairs can be found as:

\[ 1 \times 103 = 103 \]

The possible factor pair of 103 is given as (1, 103).

All these numbers in pairs, when multiplied, give 103 as the product.

The negative factor pairs of 103 are given as:

\[ -1 \times -103 = 103 \]

It is important to note that in negative factor pairs, the minus sign has been multiplied by the minus sign due to which the resulting product is the original positive number. Therefore, -1, and -103 are called negative factors of 103.

The list of all the factors of 103 including positive as well as negative numbers is given below.

Factor list of 103 : 1, -1, 103, and -103

Factors of 103 Solved Examples

To better understand the concept of factors, let’s solve some examples.

Example 1

How many factors of 103 are there?

Solution

The total number of Factors of 103 is 4.

Example 2

Find the sum of the factors of 103. 

Solution

The sum of factors of 103 can be obtained by adding all the factors of 103. This is shown below:

Sum = 1 + 103 = 104

So, the sum of factors of 103 is 104. 

Factors of 102

Factors of 104

Factors List

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